A Taylor expansion of the square root matrix functional

2017/05/23 by Pierre Del Moral, Del Moral, Pierre, Angèle Niclas +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #15A24 #15A60 #15B48 #Advanced Optimization Algorithms Research #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1705.08561

openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This short note provides an explicit description of the Fréchet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fréchet derivatives of the matrix square root at any order starting from the first order derivative. A Taylor expansion at any order with an integral remainder term is also provided, yielding the first result of this type for this class of matrix functional.

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